Algebra, Geometry, and Cryptology Seminar

Fall 2019

Organized by Zach Teitler <zteitler@boisestate.edu>.

Time: Fridays, 3:00-3:50
Location: MB124

View archives of past semesters

• Taking the seminar for credit
The seminar may be taken for credit as Math 498 or 598. For information about receiving credit, contact zteitler@boisestate.edu.
• Everybody is welcome!
Everybody interested is welcome to attend and participate! Enrollment for credit is not required. We welcome students to attend and present in the seminar. Attending seminars and colloquium presentations is an excellent way to learn about research topics and senior thesis topics.
• AGC Seminar mailing list
Announcements of upcoming seminars are sent by email to all interested participants. To be added to the AGC Seminar mailing list, contact zteitler@boisestate.edu.

Planning meeting

September 6

Topology Seminar

Allison Arnold-Roksandich, BSU
Normal Mathematics

Kennedy Courtney, BSU
Index and the Poincare-Hopf Theorem

September 13

Allison Arnold-Roksandich, BSU
An Introduction to Modular Forms and eta-theta Functions

Simply put, “modular forms are everywhere.” Their uses go from the abstract and theoretical (like Fermat’s Last Theorem), to encoding data (when looking at partitions), to the physical (like the study of black holes). Their presence is usually indicative of a deep underlying symmetry. This talk aims to introduce modular forms, two primary examples: Dedekind’s eta function and theta functions, and some fun results.

September 20

Tommaso de Fernex, University of Utah
A simplicity criterion for normal isolated singularities

Let $X$ be a complex variety defined in $\mathbb{C}^n$ by the vanishing of one (or more) holomorphic functions $f(z_1,…z_n)=0$, and let $P$ be a point of $X$. Assume that $X$ is smooth (i.e., a manifold) in a punctured neighborhood of $P$; $X$ is however allowed to be singular at $P$, so that this point is an isolated singularity of $X$.  The intersection of $X$ with the boundary of a small ball in $\mathbb{C}^n$ centered at $P$ is a real hypersurface in $X$ and is called the link of $P$. It is natural to ask how much information the link carries about the singularity; for instance, the link of a smooth point is a sphere, and one can ask whether the converse is true. Work of Mumford and Brieskorn has shown that this is the case for normal surface singularities but not in higher dimensions. Recently, McLean asked whether more structure on the link may provide a way to characterize smooth points. In this talk, I will give a general introduction to this circle of questions and discuss how CR geometry can be used to distinguish smooth points from their links. The proof relies on a partial solution to the complex Plateau problem, which is a complex analytic analogue of the classical Plateau problem of Lagrange.

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November 22

Topology Seminar
Uwe Kaiser, BSU
Quantum Modular Forms and Knot Invariants

November 29

No meeting this week (Thanksgiving holiday)

TBA

December 13

No meeting this week (last week of classes)